OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 1 — Jan. 12, 2004
  • pp: 11–18

Linear and nonlinear dynamics of matter wave packets in periodic potentials

Th. Anker, M. Albiez, B. Eiermann, M. Taglieber, and M. K. Oberthaler  »View Author Affiliations

Optics Express, Vol. 12, Issue 1, pp. 11-18 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (376 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We investigate experimentally and theoretically the nonlinear propagation of 87Rb Bose Einstein condensates in a trap with cylindrical symmetry. An additional weak periodic potential which encloses an angle with the symmetry axis of the waveguide is applied. The observed complex wave packet dynamics results from the coupling of transverse and longitudinal motion. We show that the experimental observations can be understood applying the concept of effective mass, which also allows to model numerically the three dimensional problem with a one dimensional equation. Within this framework the observed slowly spreading wave packets are a consequence of the continuous change of dispersion. The observed splitting of wave packets is very well described by the developed model and results from the nonlinear effect of transient solitonic propagation.

© 2004 Optical Society of America

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(270.5530) Quantum optics : Pulse propagation and temporal solitons
(350.4990) Other areas of optics : Particles

ToC Category:
Focus Issue: Cold atomic gases in optical lattices

Original Manuscript: November 11, 2003
Revised Manuscript: December 21, 2003
Published: January 12, 2004

Th. Anker, M. Albiez, B. Eiermann, M. Taglieber, and M. Oberthaler, "Linear and nonlinear dynamics of matter wave packets in periodic potentials," Opt. Express 12, 11-18 (2004)

Sort:  Journal  |  Reset  


  1. �??Bose-Einstein condensation in atomic gases,�?? ed. by M. Inguscio, S. Stringari, and C. Wieman, (IOS Press, Amsterdam 1999)
  2. F.S. Cataliotti, S. Burger, S. C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Ingusio, �??Josephson Junction Arrays with Bose-Einstein Condensates�??, Science 293 843 (2001). [CrossRef] [PubMed]
  3. A. Trombettoni and A. Smerzi, �??Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates,�?? Phys. Rev. Lett. 86 2353 (2001). [CrossRef] [PubMed]
  4. M. Steel and W. Zhang, �??Bloch function description of a Bose-Einstein condensate in a finite optical lattice,�?? cond-mat/9810284 (1998).
  5. P. Meystre, Atom Optics (Springer Verlag, New York, 2001) p 205, and references therein.
  6. The experimental realization in our group will be published elsewhere.
  7. V.V. Konotop, M. Salerno, �??Modulational instability in Bose-Einstein condensates in optical lattices,�?? Phys. Rev. A 65 021602 (2002). [CrossRef]
  8. N. Ashcroft and N. Mermin, Solid State Physics (Saunders, Philadelphia, 1976).
  9. A.A. Sukhorukov, D. Neshev, W. Krolikowski, and Y.S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically-induced lattices,�?? nlin.PS/0309075.
  10. B. Eiermann, P. Treutlein, Th. Anker, M. Albiez, M. Taglieber, K.-P. Marzlin, and M.K. Oberthaler, �??Dispersion Management for Atomic Matter Waves,�?? Phys. Rev. Lett. 91 060402 (2003). [CrossRef] [PubMed]
  11. M. Kozuma, L. Deng, E.W. Hagley, J.Wen, R. Lutwak, K. Helmerson, S.L. Rolston, andW.D. Phillips, �??Coherent Splitting of Bose-Einstein Condensed Atoms with Optically Induced Bragg Diffraction,�?? Phys. Rev. Lett. 82 871(1999). [CrossRef]
  12. B.P. Anderson, and M.A. Kasevich, �??Macroscopic Quantum Interference from Atomic Tunnel Arrays,�?? Science 282 1686 (1998); [CrossRef] [PubMed]
  13. O. Morsch, J. M¨uller, M. Cristiani, D. Ciampini, and E. Arimondo, �??Bloch Oscillations and Mean-Field Effects of Bose-Einstein Condensates in 1D Optical Lattices,�?? Phys. Rev. Lett. 87 140402 (2001). [CrossRef] [PubMed]
  14. C.F. Bharucha, K.W. Madison, P.R. Morrow, S.R.Wilkinson, Bala Sundaram, and M.G. Raizen, �??Observation of atomic tunneling from an accelerating optical potential,�?? Phys. Rev. A 55 R857 (1997) [CrossRef]
  15. L. Salasnich, A. Parola, and L. Reatto, �??Effective wave equations for the dynamics of cigar-shaped and diskshaped Bose condensates,�?? Phys. Rev. A 65 043614 (2002). [CrossRef]
  16. G.P. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, San Diego, 2001).
  17. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 1995).
  18. R.G. Scott, A.M. Martin, T.M. Fromholz,S. Bujkiewicz, F.W. Sheard, and M. Leadbeater, �??Creation of Solitons and Vortices by Bragg Reflection of Bose-Einstein Condensates in an Optical Lattice,�?? Phys. Rev. Lett. 90 110404 (2003). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1. Fig. 2. Fig. 3.
Fig. 4.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited